Numerical analysis of a nonlinear evolutionary system with applications in viscoplasticity

We consider numerical approximations of a class of abstract nonlinear evolutionary systems arising in the study of quasi-static frictional contact problems for elastic-viscoplastic materials. Both semidiscrete and fully discrete schemes are analyzed. Strong convergence of both approximations is established under minimal solution regularity. The results are applied to two particular frictional contact problems for viscoplastic bodies, where the finite element method is employed to discretize the spatial domain. Under additional regularity assumptions on the exact solution, some error estimates are derived.